Obama has tried to make clear that the number of troops he is sending is the minimum number he needs to accomplish US goals through his strategy. By taking his time to decide on this level and by consulting with many leaders on the subject, he hoped to convey that the decision was well thought out.
However, recent polls show that the public may not be entirely supportive or have confidence in the President's new plan. Much of the President's speech was focused on narrowing the scope of US goals in Afghanistan. Instead of nation building, the President outlined a plan to dismantle and disrupt al Qaeda, which has a focus of building up the Afghan national army and police. Despite the narrower focus, only 48% of Americans say the US is certain or likely to meet its goals in Afghanistan. Although this number may not reflect American's faith in Obama, Obama's scaling back goals in Afghanistan points towards his focus on public opinion and increasing public support for the war.
Some have even criticized the speech, saying Obama has pandered to all groups, yet has really satisfied no one yet. One European viewpoint found in Der Spiegel said, "Never before has a speech by President Barack Obama felt as false as his Tuesday address announcing America's new strategy for Afghanistan.... It left both dreamers and realists feeling distraught." But attempting to appeal to all groups without fully satisfying any group is just a part of diplomacy, and before criticizing the speech, critics should acknowledge the difficulties associated with the situation at hand.
Nevertheless, Obama is realizing that the entire public will not be satisfied with executive policy decisions no matter how well-thought they are. But that's not to argue against prudent decision-making. In the end, Obama's decision will be judged based on its success.